Question

Michael’s backyard is in the shape of an isosceles trapezoid and has a semicircular patio as shown in the diagram below. (image attached)On a windy fall day, a leaf lands randomly in Michael's backyard. Which is the closest approximation of the probability that the leaf lands somewhere in the section of the backyard represented by the shaded region in the diagram?A. 15%B. 30%C. 70%D. 85%thank you ! :)

Answer 1

1. Find the area of the backyard:

$\begin{gathered} A=\frac{(base1+base2)}{2}*h \\ \\ A=\frac{65ft+30ft}{2}*50ft \\ \\ A=\frac{95ft}{2}*50ft \\ \\ A=2375ft^2 \end{gathered}$

2. Find the area of the patio:

$\begin{gathered} A=\frac{\pi *r^2}{2} \\ \\ A\approx\frac{3.14*(15ft)\placeholder{⬚}^2}{2} \\ \\ A\approx\frac{3.14*225ft^2}{2} \\ \\ A\approx353.25ft^2 \end{gathered}$

3. Find the area of the shaded region:

$A_{shaded}=2375ft^2-353.25ft^2=2021.75ft^2$

4. Find the probability that the leaf falls in the shaded region known that the total area (100%) is 2375 suqare feet:

$P=\frac{shaded\text{ Area}}{total\text{ Area}}*100=\frac{2021.75ft^2}{2375ft^2}*100\approx85$

Then, the probability is approximately 85%

Answer D